The main difference is that people buy a newspaper for the information it publishes while people join a social network because their friends are there. A social network starting to editorialize content is therefore a problem since there is really no alternative ways to keep in touch with friends as effectively, meaning these social networks gets to force their opinions on people.
Who is forcing a private organization to adopt any stance? "Leaving alone" is not the same as "actively promoting." Twitter leaving alone a story does not mean Twitter is promoting that story, that is exactly what section 230 is about.
> not to force the existing ones to promote what we believe is right.
I guess they don't need to pay taxes either, or take a stand against violence, or racism, or....? They still exist within the society in which they function and that means both social and legal rules bind them, same as you or me. Despite abundant evidence to the contrary, their status as a corporation doesn't somehow entitle them to a more special or louder voice than any one else's.